Not necessarily. There are some interesting potential radiation issues with "warp drives" as well. For example, at the boundary of a warp bubble of the generally-Alcubierre-like variety, space is shearing / expanding such that virtual particle pairs are incapable of recombining, just like at an event horizon. That could potentially create a great deal of radiation draining energy from the warp field.
Additionally, what happens to particles that are intercepted by the travelling bubble? They don't just disappear!
(Essentially, particles encountered en-route pile up near the boundary and are released in a large burst when you turn the thing off, which is potentially very bad for the local environment, of which you are a part.)
